The error-in-rejection probability of meta-analytic panel tests

Abstract

Meta-analytic panel unit root tests such as Fisher’s Chi^2 test, which consist of pooling the p-values of time series unit root tests, are widely applied in practice. Recently, several Monte Carlo studies have found these tests’ Error-in-Rejection Probabilities (or, synonymously, size distortion) to increase with the number of series in the panel. We investigate this puzzling finding by modelling the finite sample p-value distribution of the time series tests with local deviations from the asymptotic p-value distribution. We find that the size distortions of the panel tests can be explained as the cumulative effect of small size distortions in the time series tests.